Optimal Rebate Strategies Under Dynamic Pricing

Abstract

Instant discounts and mail-in rebates are two common pricing tools in retail, but they are not simple substitutes. On the one hand, consumers discount the face value of a mail-in rebate, making it less effective than an instant discount in inducing consumers’ purchase. On the other hand, a portion of consumers with mail-in rebates fail to redeem them, resulting in savings for the retailer. We study how retailers, under pressure to move inventory, should use these two pricing tools to maximize revenue by determining the optimal use of mail-in rebates together with dynamic pricing of limited inventory. In a base model that allows frequent adjustment of product price and rebate face value, the optimal policy takes the form of “discount only,” “rebate only,” or a combination of the two. For useful heuristics with infrequent policy adjustment, we analyze the deterministic approximation of the base model. Interestingly, the deterministic solution splits the selling season into two segments, and it suggests using different pricing-rebate policies in each segment. Finally, we study a scenario in which the retailer has only one opportunity to introduce a static rebate, and we find that for any inventory level there is a cutoff time before which rebates should not be used. Our numerical studies show that such an optimal one-time static rebate policy performs well compared with the optimal revenue in the benchmark model.

Keywords: dynamic programming: applications, optimal control, inventory/production: policy: maketing/pricing Area of Review: Operations and Supply Chains revenue management, dynamic pricing, rebate coupon, heuristics, asymptotic optimality